WASHINGTON — Paul D. Ryan, a son and grandson of Midwestern lawyers, ascended rapidly in American politics as a man with big plans: to overhaul the tax code, slash federal spending and rewrite the social contracts for Medicare and Social Security.

Mr. Ryan, 45, who was elected in a celebratory Capitol Hill pageant on Thursday as the 54th speaker of the House, the youngest to grip the gavel since the late 1860s, now confronts a fundamental question: Will his new post provide a platform to pursue his bold visions for a renewed America, or will those big ideas weigh him down in an era defined by confrontation and small-bore compromises?

Recent experience, including the success of Democrats in blocking all of Mr. Ryan’s sweeping budget proposals, suggests that he will continue to harbor expansive aspirations but will have little choice but to set more modest goals.

Mr. Ryan not only faces the realities of divided government, at least for the next 14 months, but also must try to repair the deep fractures among House Republicans — a point that he acknowledged in his opening remarks: “The House is broken. We are not solving problems. We are adding to them.”

Many eyes in the House chamber lingered on a cluster of hard-line rank-and-file conservatives who forced the departure of Mr. Ryan’s predecessor, John A. Boehner of Ohio. On Thursday, those hard-liners joined the standing ovation for Mr. Ryan.

They have been demanding that he carry out an array of changes in House rules to empower individual lawmakers. The hard-line House Freedom Caucus, splintering under pressure from fellow Republicans, hardly had the votes to derail Mr. Ryan’s rise, and he appeared to outfox them, at least briefly, by demanding unity before he agreed to accept the gavel.

Representative John Fleming, Republican of Louisiana, who helped found the caucus, flashed the new speaker a thumbs-up as Mr. Ryan made his way down the aisle to the rostrum and an emotional hug with a weepy Mr. Boehner. Several of the conservatives said they were prepared to give Mr. Ryan the benefit of the doubt, at least for now.

“He’s just as frustrated as we have been with the process,” said Representative Raúl R. Labrador, of Idaho, one of the leaders of the Freedom Caucus. “He wants to change business as usual. So we’re cautiously optimistic that he’s going to change the way we’re doing things here, and we’re going to give him a chance.”

Photo

Paul D. Ryan, center, in Washington on Thursday. “We have nothing to fear from honest differences, honestly stated,” he said after being elected House speaker.Credit
Stephen Crowley/The New York Times

While Mr. Boehner, 65, came into the job as a seasoned leader who tried, unsuccessfully in the end, to appease the Tea Party members, Mr. Ryan, who was the Republican Party’s vice-presidential nominee in 2012, represents a new generation.

His youth was underscored by his three children — 13, 12 and 10 — tucked into the seats high above the chamber floor next to their mother, Janna. His experience on the national stage was recalled by the two guests who sat behind his family: a former Massachusetts governor and Republican presidential nominee, Mitt Romney, who asked Mr. Ryan to be his running mate, and Mr. Romney’s wife, Ann.

Democrats, while praising Mr. Ryan’s willingness to cooperate with them in the past, were also poised to typecast him as a big-thinking public servant with fine talking points, but who will ultimately fall back on the trickle-down economics of the Reagan era that they say will help neither the poor nor the middle class.

“This presents this clearest distinction of anyone they could have named: the Ryan budget,” the House Democratic leader, Representative Nancy Pelosi of California, said in an interview. “Eight-hundred-billion-dollar cuts in Medicare; big tax breaks to the wealthiest people; voucherizing Medicare, not giving a guarantee; block-granting Medicaid, which 65 to 70 percent goes to seniors for long-term health care.”

“A budget is supposed to be a statement of values about our country,” Ms. Pelosi added. “So it will be interesting to see if now, in the position of speaker, if those will still be his priorities, and if so, we welcome the debate on the substance.”

Yet it was Mr. Ryan who negotiated for Republicans in reaching a crucial budget accord after a damaging government shutdown in 2013, curtailing expectations but ultimately clinching a deal that he noted “was small in substance but big in symbolism.”

“We spoke of having to scale back our ambitions,” Mr. Ryan wrote of his negotiations with Senator Patty Murray, Democrat of Washington, “from trying to score a touchdown, to getting a first down, to just getting positive yardage.”

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“When we tried to go big, we realized we were on different teams with different end zones,” Mr. Ryan, a lifelong Green Bay Packers fan, wrote, continuing the football metaphor in his 2014 book, “The Way Forward.” “But there was in fact common ground.”

By his own account, Mr. Ryan, who was elected to the House in 1998 at age 28, is a somewhat accidental traveler in the corridors of power, one whose passion lies in the grinding details of policy prescriptions and budget scores.

Ms. Pelosi said she hoped Mr. Ryan would be inspired by his own publicly declared desire to spend time with his children to pursue legislation that would grant paid leave to American workers for child care, and provide other benefits for middle-class families.

“I hope that he would translate his personal value into public policy to enable people to have paid leave if their child is sick,” she said.

For better or worse, colleagues say, Mr. Ryan, who spends weekends with his family in Janesville, Wis., believes in the policy proposals that he puts forward and, more important, in the social values they are rooted in.

A Roman Catholic and former altar boy, Mr. Ryan has written and spoken extensively about his belief that private, voluntary charity can do a better job than government in helping the poor and other needy Americans.

Mr. Ryan’s ideas are not just about the dollars and cents of taxes and spending. He has expressed a willingness to work with Democrats on immigration issues that some of his more conservative colleagues find troubling.

In his book, he lays out a vision for overhauling antipoverty and other social welfare programs that at times seems to blend elements of Lyndon B. Johnson’s Great Society with the conservative-libertarian philosophies and market-based approaches of Jack F. Kemp, the longtime New York congressman who was a hero and mentor or Mr. Ryan.

“Today, there are at least 92 federal programs that claim to help the poor,” Mr. Ryan wrote. “We spent $799 billion on them in 2012 alone. And yet, the official poverty rate is the highest it has been in 21 years.”

While Republicans praise Mr. Ryan as perhaps their party’s best “ideas man,” some colleagues said that when Mr. Ryan was afforded his best chance to potentially advance sweeping fiscal reforms — as a member in 2010 of the National Commission on Fiscal Responsibility and Reform, a bipartisan panel — he ultimately chose partisan politics and Republican unity over a potentially far-reaching compromise.

“We had an opportunity,” former Senator Kent Conrad, Democrat of North Dakota, who served with him on the panel, said in a recent interview. “We would have fixed Social Security. We would have fixed the long-term imbalances the country is facing. We would have improved Medicare. It would have put America in a position to have a resurgence. It would have put confidence in our institutions.”

Mr. Conrad added, “Paul really, I think, failed that test.”

To a large degree, the budget accord reached this week, which Mr. Ryan voted to support, will free him from any immediate need to pursue his most ambitious fiscal proposals, and it should clear some room for him to focus on some of the nuts-and-bolts complaints about how the House operates that have divided Republicans.

Mr. Ryan, in his speech, called for a more conciliatory approach. “We have nothing to fear from honest differences, honestly stated,” he told his colleagues. “If you have ideas, let’s hear them. I believe a greater clarity between us can lead to a greater charity among us.”

“I believe, with every fiber of my being, we can renew the ‘America Idea,’ ” he said later, adding: “Let’s seize the moment. Let’s rise to the occasion.”

A version of this article appears in print on October 30, 2015, on Page A1 of the New York edition with the headline: As Speaker, Ryan May Need to Pare Lofty Goals . Order Reprints|Today's Paper|Subscribe